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You may need to use the appropriate appendix table or technology to answer this question. Software...

You may need to use the appropriate appendix table or technology to answer this question. Software companies work hard to produce software that does not have bugs in it. The average number of bugs found in a new software program at its inception is 26.5 with a standard deviation of 3.5 bugs. A random sample of size 45 software programs was examined. (a) Determine the mean (in bugs) of the sampling distribution of the sample mean for samples of size 45. .58 bugs (b) Calculate the standard deviation (in bugs) of the sampling distribution of the sample mean of samples of size 45. (Round your answer to three decimal places.) bugs (c) The shape of the sampling distribution of the sample mean is approximately normal. Which of the following choices justifies that statement? We have sampled less than 10% of the population. A random sample was taken. Tchebysheff's Theorem tells us that the distribution is approximately normal. The sampling distribution of the sample mean is always normally distributed. The population is approximately normally distributed. The sample size is 30 or more, so the Central Limit Theorem tells us that the distribution is approximately normal. (d) What is the probability that in a random sample of size 45 software programs, the company would find an average of 27 or more bugs? (Round your answer to four decimal places.)

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